I've done quite a lot of reading about stool because it's really a great indicator of all around health. From what I've read over the past year, the main concern with stool is color. Anything else is of little importance. Just make sure the color is normal. Green means the stool is moving through the system too fast. Yellow can mean the same thing although sometimes, they say. it can be an indicator of liver, gallbladder, or pancreas problems. I wouldn't worry too much about yellow though because in all honesty it's most likely just the stool moving too fast through the system as well. Bile is what gives stool it's color. Bile starts out green, turns yellow, then finely brown.
I'm sure if you've ever seen a dog throw up bile it's been bright yellow.
The most serious concern, and I mean if you see this in your or your dogs stool you need to rush to a doctor or vet IMMEDIATELY, is if the stool is white or clay color. This is a serious problem with the gallbladder or liver. Like a blockage, or the liver isn't producing enough bile, or something even as horrible as a tumor blocking the way for the bile to be released. I saw this with my own dog when he had liver and gallbladder issues and I never thought anything of it. I thought it was because I started feeding him chicken that his stool was lighter. Big mistake and I feel like an idiot for it but I didn't know any better at the time. NEVER take white or clay stools lightly, it is absolutely serious. The quicker you get yourself or your dog looked at the better. With feeding raw and bone it might be hard to evaluate the whiteness of a stool because the bone can cause stool to look white. I'm not telling you to evaluate your dogs stool by digging through it or anything but hopefully you can tell the difference between white bone and white stool. There should be some brown stool somewhere with the whiteness of the bone lol.
Shape and size is of little concern. Obviously with feeding raw I'm sure you know that. My dog used to poop a lot, even on a higher quality, high protein kibble. It went from 3 times a day to two and VERY little. Usually one larger poo and then maybe like a couple little "pebbles" at night. He's even skipped his 2nd poo sometimes and at first I was really concerned but it happens occasionally. The only time he ever has larger poos is when I add in something, like giving him frozen carrots for teeth cleaning, it goes in one way and right out the other.
As far as mucus is concerned. It's a natural part of the intestinal tract. There's this whole new health thing going on where people are taking colon cleanses and all this crap to get rid of that build up of mucus and toxins. If that's what people want to do so be it but it's idiotic. The mucus is essential to the stool being able to move through the intestines smoothly. If you eat a healthy diet the mucus will naturally be removed from the colon by eating fiber, vegies, esc. I would never be concerned about mucus in stool on less it's accompanied by other symptoms which could be an indicator of IBS, Crohn's, or Colitis which are conditions associated with mucus in stool.
I mentioned the colon cleansing thing for a reason though, because I think that might be a reason the mucus is possibly showing up in the dogs stool. With certain colon cleanses people eat things like oatmeal and a lot of soluble fiber filled foods which scrape the intestinal walls clean of mucus so that it comes out of the body with the stool. Since bones would absolutely be capable of doing just the same thing as oatmeal, if not better, that could be the explanation behind the mucus. The raw bone is basically just scraping out the mucus from the colon and that could mean there was an excess amount of mucus in your dogs colon and the raw bone is now effectively removing it. I wouldn't be concerned unless this continues to go on for a longer period of time or there are other symptoms as well. If that's the case it might be IBS or something else but I wouldn't over worry about it now.